In a signed binary, the first bit (the leftmost) is reserved for the sign,
1 = negative, 0 = positive. This bit does not count when calculating the absolute value.
2. Construct the unsigned binary number.
Exclude the first bit (the leftmost), that is reserved for the sign:
1011 0000 1010 0111 = 011 0000 1010 0111
3. Map the unsigned binary number's digits versus the corresponding powers of 2 that their place value represent:
214
0 213
1 212
1 211
0 210
0 29
0 28
0 27
1 26
0 25
1 24
0 23
0 22
1 21
1 20
1
4. Multiply each bit by its corresponding power of 2 and add all the terms up.
011 0000 1010 0111(2) =
(0 × 214 + 1 × 213 + 1 × 212 + 0 × 211 + 0 × 210 + 0 × 29 + 0 × 28 + 1 × 27 + 0 × 26 + 1 × 25 + 0 × 24 + 0 × 23 + 1 × 22 + 1 × 21 + 1 × 20)(10) =
(0 + 8 192 + 4 096 + 0 + 0 + 0 + 0 + 128 + 0 + 32 + 0 + 0 + 4 + 2 + 1)(10) =
(8 192 + 4 096 + 128 + 32 + 4 + 2 + 1)(10) =
12 455(10)
5. If needed, adjust the sign of the integer number by the first digit (leftmost) of the signed binary:
1011 0000 1010 0111(2) = -12 455(10)
The number 1011 0000 1010 0111(2) converted from a signed binary (base two) and written as an integer in decimal system (base ten):
1011 0000 1010 0111(2) = -12 455(10)
Spaces were used to group digits: for binary, by 4, for decimal, by 3.